Invasion and fixation of microbial dormancy traits under competitive pressure |
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Institution: | 1. Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands;2. Delft Institute of Applied Mathematics, Technical University Delft, Delft, The Netherlands;3. Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL, USA;4. Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, FL, USA;5. Department of Diagnostic Imaging and Interventional Radiology, Moffitt Cancer Center & Research Institute, Tampa, FL, USA;6. Department of Genitourinary Oncology, Moffitt Cancer Center & Research Institute, Tampa, FL, USA |
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Abstract: | Microbial dormancy is an evolutionary trait that has emerged independently at various positions across the tree of life. It describes the ability of a microorganism to switch to a metabolically inactive state that can withstand unfavourable conditions. However, maintaining such a trait requires additional resources that could otherwise be used to increase e.g. reproductive rates. In this paper, we aim for gaining a basic understanding under which conditions maintaining a seed bank of dormant individuals provides a “fitness advantage” when facing resource limitations and competition for resources among individuals (in an otherwise stable environment). In particular, we wish to understand when an individual with a “dormancy trait” can invade a resident population lacking this trait despite having a lower reproduction rate than the residents. To this end, we follow a stochastic individual-based approach employing birth-and-death processes, where dormancy is triggered by competitive pressure for resources. In the large-population limit, we identify a necessary and sufficient condition under which a complete invasion of mutants has a positive probability. Further, we explicitly determine the limiting probability of invasion and the asymptotic time to fixation of mutants in the case of a successful invasion. In the proofs, we observe the three classical phases of invasion dynamics in the guise of Coron et al. (2017, 2019). |
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Keywords: | Dormancy Seed bank Competition-induced switching Individual-based stochastic population model Multitype branching process Lotka–Volterra type system |
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